A Student’s Solutions Manual to Accompany ADVANCED ENGINEERING MATHEMATICS, 8TH EDITION PETER V. O’NEIL

A Student’s Solutions Manual to Accompany
ADVANCED ENGINEERING MATHEMATICS,
8TH EDITION
PETER V. O’NEIL

,
, STUDENT'S SOLUTIONS MANUAL
TO ACCOMPANY




AdvancedEngineering
Mathematics
8th EDITION




PETER V. O’NEIL

, Contents




1 First-Order Differential Equations 1
1.1 Terminology and Separable Equations
cf 1
1.2 The
cf Linear
c f c f First-Order
c f c f Equation
c f c f 8
1.3 Exact Equations
cf 11
1.4 Homogeneous, Bernoulli and Riccati Equations
cf c f c f c f c f c f c f c f c f 15
2 Second-Order Differential
c f c f Equations
c f c f 19
2.1 The Linear Second-Order Equation
cf c f cfcf c f 19
2.2 The Constant Coefficient Homogeneous Equation
cf 21
2.3 Particular Solutions of the Nonhomogeneous Equation
cf 24
2.4 The Euler Differential Equation
cf 27
2.5 Series Solutions
cf c f c f 29
3 The Laplace Transform 35
3.1 Definition and Notation
cf 35
3.2 Solution of Initial Value Problems
cf 37
3.3 The Heaviside Function and Shifting Theorems
cf 40
3.4 Convolution
cf 44
3.5 Impulses and the Dirac Delta Function
cf 48
3.6 Systems of Linear Differential Equations
cf 48

iii